Benchmark study of an auxiliary-field quantum Monte Carlo technique for the Hubbard model with shifted-discrete Hubbard-Stratonovich transformations

Seki, Koh‐ichi; Sorella, Sandro

doi:10.1103/physrevb.99.144407

Cited by 8 publications

(1 citation statement)

References 70 publications

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“…( 9) becomes site dependent as α → α i = arccos (e −g i /2 ). We also note that the site-dependent chemical potential or "fugacity" factors in the Gutzwiller factor [112] can also be included if a generalization of the discrete Hubbard-Stratonovich transformation [113] is employed. It is also possible to extend the Gutzwiller factor to the Jastrow operator, which takes into account long-range density-density correlations [114], and to imaginary-time-evolution operators for electron-phononcoupled systems [115][116][117], by using different kinds of Hubbard-Stratonovich transformations.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation

Seki,

Otsuka,

Yunoki

2022

Preprint

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We propose a quantum-classical hybrid scheme for implementing the nonunitary Gutzwiller factor using a discrete Hubbard-Stratonovich transformation, which allows us to express the Gutzwiller factor as a linear combination of unitary operators involving only single-qubit rotations, at the cost of the sum over the auxiliary fields. To perform the sum over the auxiliary fields, we introduce two approaches that have complementary features. The first approach employs a linear-combination-of-unitaries circuit, which enables one to probabilistically prepare the Gutzwiller wave function on a quantum computer, while the second approach uses importance sampling to estimate observables stochastically, similar to a quantum Monte Carlo method in classical computation. The proposed scheme is demonstrated with numerical simulations for the half-filled Fermi-Hubbard model. Furthermore, we perform quantum simulations using a real quantum device, demonstrating that the proposed scheme can reproduce the exact ground-state energy of the two-site Fermi-Hubbard model within error bars.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation

Seki,

Otsuka,

Yunoki

2022

Preprint

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Apical oxygen vibrations dominant role in d-wave cuprate superconductivity and its interplay with spin fluctuations

Rosenstein¹,

Shapiro²

2021

J. Phys. Commun.

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Microscopic theory of a high T c cuprate Bi 2 Sr 2 CaCu 2 O 8+x based on main pairing channel of electrons in CuO planes due to 40mev lateral vibrations of the apical oxygen atoms in adjacent the SrO ionic insulator layer is proposed. The separation between the vibrating charged atoms and the 2D electron gas creates the forward scattering peak leading in turn to the d -wave pairing within Eliashberg formalism. The phonon mode naturally explain the kink in dispersion relation observed by ARPES and the and effect of the O 16 → O 18 isotope substitution in the normal state. To describe the pseudogap physics a single band fourfold symmetric t − t ′ Hubbard model, with the hopping parameters t ′ ∼ − 0.17 t and the on site repulsion e U ∼ 6t. It described the Mott insulator at low doping, while at higher dopping the pseudogap physics (still strongly correlated) can be be approximated by the symmetrized mean field model and with renormalized U incorporating screening. The location of the transition line T *between the locally antiferromagnetic pseudogap and the paramagnetic overdoped phases and susceptibility (describing spin fluctuations coupling to 2DEG) are also obtained within this approximation. The superconducting d - wave gap mainly due to the phonon channel but is assisted by the spin fluctuations (15%–20%). The dependence of the gap and T c on doping and effect of the isotope substitution are obtained and is consistent with experiments.

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Efficient method for grand-canonical twist averaging in quantum Monte Carlo calculations

Azadi

Foulkes

2019

Phys. Rev. B

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We introduce a simple but efficient method for grand-canonical twist averaging in quantum Monte Carlo calculations. By evaluating the thermodynamic grand potential instead of the ground state total energy, we greatly reduce the sampling errors caused by twist-dependent fluctuations in the particle number. We apply this method to the electron gas and to metallic lithium, aluminum, and solid atomic hydrogen. We show that, even when using a small number of twists, grand-canonical twist averaging of the grand potential produces better estimates of ground state energies than the widely used canonical twist-averaging approach. arXiv:1910.06814v1 [cond-mat.mtrl-sci]

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Benchmark study of an auxiliary-field quantum Monte Carlo technique for the Hubbard model with shifted-discrete Hubbard-Stratonovich transformations

Cited by 8 publications

References 70 publications

Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation

Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation

Apical oxygen vibrations dominant role in d-wave cuprate superconductivity and its interplay with spin fluctuations

Efficient method for grand-canonical twist averaging in quantum Monte Carlo calculations

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